How to properly combine Z passes using multiple .EXR files?
The general problem with EXR images, is that they don't really behave as a normal image (like PNG). A PNG has, for each color, a min value 00 and a max value FF. An EXR is just a mathematical value from 0 up to infinity for each pixel.

So rather than using multiply (as you are doing, and which works for PNG images), you should use minimum (or maximum,depending on the base layer you are using). And repeat the process for each subframe/tile.

The end result will be a complete image with values ranging from 0 till...



You can then use normalise to change these values to something that represents an image (from 00 till FF). 

Tip: make sure you don't use normalise on your subframe EXR or all of them will go from white (clearest point) to black (furthest point) for each subframe rather than 1 time for the complete image.